Software defined radio

ABSTRACT

A software defined radio is disclosed. The software defined radio may utilize a method for encoding a bit stream into non-periodic spiral-based symbol waveforms for transmission and reception. The method includes transmitting a signal constructed from one or more non-periodic modulation sets residing on a memory system of the software defined radio, where each modulation set corresponds to a symbol alphabet and provides non-periodic symbol waveforms corresponding to symbol bit sequences segmented by a microprocessor according to alphabet size. The method also includes receiving the signal constructed from one or more spiral modulation sets, wherein the signal from one or more spiral modulation sets are filtered and then fed to an analog to digital converter, where the signal constructed from the one or more spiral modulation sets is digitized and are fed to the microprocessor. A non-transitory computer storage media may also execute the method.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/774,253 filed Mar. 7, 2013 and entitled APPLICATIONS OFNON-PERIODIC SIGNALS, the entire contents of which are herebyincorporated by reference

BACKGROUND

The utilization of non-periodic functions for telecommunicationsignaling may utilize waveforms derived from functions in either of thetwo equivalent forms:

$\begin{matrix}{{f_{g}(t)} = {^{t \cdot {\cos {({2^{1 - g}\pi})}}}^{ \cdot t \cdot {\sin({2^{1 - g}\pi}\;)}}}} & (1) \\{or} & \; \\{{f_{g}(t)} = ^{t\; ^{(2^{2 - g})}}} & (2)\end{matrix}$

In these equations, i is the imaginary constant equal to √{square rootover (−1)}, t is the time parameter, and g has the effect of varying thegeometry of the waveform where g=2 corresponds to a complex circle, asthe above reduce to the Euler term e^(ti). Known techniques such asQuadrature Amplitude Modulation or QAM are based on complex circles.Values of g>2 correspond to complex spirals of increasingly rapid growthand increasingly lower frequency.

There are other variations of these waveforms based on alteringparameters including but not limited to amplitude, frequency, phase,signal duration and direction of rotation. There is also a unified wayof specifying many possible variations of waveforms via the generalizedspiral formula:

$\begin{matrix}{{f_{g}(t)} = {\left\lbrack {\kappa_{0}^{\; \omega_{0}}} \right\rbrack ^{{\lbrack{\kappa_{1}^{\; \omega_{1}}}\rbrack}{({t + t_{0}})}^{{\lbrack{\kappa_{2}^{\; \omega_{2}}}\rbrack}{(2^{2 - g})}}}}} & (3)\end{matrix}$

Dropping the square brackets for conciseness, the general spiral formula(Equation 3) may be written as:

$\begin{matrix}{{f_{g}(t)} = {\kappa_{0}^{\; \omega_{0}}^{\kappa_{1}{^{\; \omega_{1}}{({t + t_{0}})}}^{\kappa_{2}^{{{\omega}\; 2{(2^{2 - g})}}\;}}}}} & (4)\end{matrix}$

The scope of this formula may be characterized by the effect of varyingits parameters on the set of symbol waveforms that may be generated. Theeffects of varying the parameters include amplitude modulation thatutilizes multiple values of κ₀, phase modulation that utilize multiplevalues of ω₀, time reversal that utilize κ₁=±1, or equivalently ω₁=0 andω₁=a, frequency modulation that has a scale κ₁, time shifts that utilizemultiple values of t₀, rotational reversal that utilize κ₂=±1, orequivalently ω₂=0 and ω₂=π, waveform shape modulation that vary g withhigher values of g that correspond to more rapid growth and lowerfrequency and other variations with general values of κ₂, e₁, and ω₂.

For the case of g=2, corresponding to the standard telecommunicationsconditions of no amplitude growth, the only parameters that are usuallymodified are amplitude, frequency and phase. By contrast, for signalswhere g>2, the generalized spiral formula shows that there areadditional parameters, or degrees of freedom, available for encodinginformation in the signal. Of particular practical significance are timereversal, rotational reversal and waveform shape modulation.

The effect of these three additional degrees of freedom is todramatically increase the number of possible modulation sets for aparticular alphabet size. By way of example, consider a communicationschannel with an alphabet size of M=8, such that three bits are encodedper symbol. For non-spiral based communications, utilizing the standardtechnique of superposition of the I & Q waveforms, the possiblemodulation sets are shown in Table 1.

TABLE 1 Non-spiral modulation sets for an alphabet of 8 PhasesAmplitudes Frequencies Symbols 8 1 1 8 4 2 1 8 4 1 2 8 2 2 2 8 2 4 1 8 21 4 8 1 8 1 8 1 4 2 8 1 2 4 8 1 1 8 8

Thus one could encode the alphabet utilizing eight phases, one amplitudeand one frequency (e.g. what is generally known as 8-PSK), or one couldutilize four phases, two amplitudes and one frequency which if it wasutilized practically would be referred to as 8-QAM and so on. As shownin Table 1 there are just ten possible modulation sets for non-spiralmodulation for M=8.

For values of g>2, one may utilize time reversal to double the number ofsymbols, and then also utilize rotation reversal to double the number ofsymbols again. Thus for a particular value of growth g, the possiblemodulation sets are shown in Table 2.

TABLE 2 Spiral modulation sets for an alphabet of 8 and just one growthvalue. Phases Amplitudes Frequencies Rotation Time Symbols 8 1 1 0 0 8 42 1 0 0 8 4 1 2 0 0 8 2 2 2 0 0 8 2 4 1 0 0 8 2 1 4 0 0 8 1 8 1 0 0 8 14 2 0 0 8 1 2 4 0 0 8 1 1 8 0 0 8 8 1 1 0 0 8 4 2 1 0 0 8 4 1 2 0 0 8 41 1 1 0 8 4 1 1 0 1 8 2 2 2 0 0 8 2 4 1 0 0 8 2 1 4 0 0 8 2 2 1 1 0 8 22 1 0 1 8 2 1 2 1 0 8 2 1 2 0 1 8 2 1 1 1 1 8 1 8 1 0 0 8 1 4 2 0 0 8 12 4 0 0 8 1 1 8 0 0 8 1 4 1 1 0 8 1 4 1 0 1 8 1 2 1 1 1 8 1 1 4 1 0 8 11 4 0 1 8 1 1 2 1 1 8

As shown in Table 2, there are approximately 32 different modulationsets for spiral-based communications with an 8-symbol alphabet. However,this represents approximately 32 possible combinations for just a singlevalue of growth “g”. Practical values of “g” vary from approximately 2.1to 3.0, with noticeable differences being observable at steps ofapproximately 0.05. I.e., a symbol set with a g value of approximately2.60 will exhibit noticeably different properties when compared to asymbol set with a g value of approximately 2.65. As such there areapproximately [2.1 3.0 0.05]=18 useful values of g, giving an overallnumber of modulation combinations for an 8-symbol alphabet ofapproximately 32*18=576. This is 576/10=58 times more combinations whencompared to non-spiral communications given an 8-symbol alphabet.

For larger alphabet sizes such as approximately 64, the number ofpossible modulation sets becomes enormous for spiral based modulation.While the mathematics behind spiral based communications is complex, theimplementation need not be. For the transmitter, the result of themathematics may be a simple lookup table which is indexed by symbolnumber and time. These values are sent to a Digital-Analog Converter orDAC whose output feeds into a radio frequency or RF stage which istypically either a mixer or directly into a power amplifier. The symbolsare transmitted across the communications channel, and a version of thesymbols generally corrupted by channel conditions is digitized at thereceiver. The digitized symbols may then be fed through a series ofmatched filters in order to determine the received symbol.

It may be desirable for a communication system to use differentmodulation sets at different times, either due to changing channelconditions or for enhanced security. From an implementation perspective,a spiral based transceiver may evaluate at run time the complexequations necessary for synthesizing the transmitter look-uptable/receiver matched filter coefficients and thus generate thenecessary data on the fly, or have the data for the various modulationsets computed off line and the results simply stored in the memorysystem.

For a typical application with an alphabet size of approximately 64, andapproximately 32 samples per symbol, the transmitter look-up tableincludes just 64*32=2048 values, with each value being typicallyrepresented by approximately 16 bits, giving a table size ofapproximately 4096 bytes per modulation set. Thus in typical memorysystem sizes available today, it is possible to store thousands ofpossible modulation sets and thus the latter approach of pre-computingmodulation set data makes more sense.

A further benefit of storing thousands of modulation sets in memory isthat it permits modulation sets to be instantaneously switched. Thisresults in significant benefits as will be described. To comprehend thevalue of switching modulation, it is helpful to know some empiricalresults of investigations into spiral based modulation. Different spiralmodulation combinations have markedly different characteristics in thepresence of various channel impairments. For example, some modulationcombinations work better with Additive White Gaussian Noise or AWGN,whereas others perform better in the presence of coherent noise. For agiven channel impairment (e.g. coherent noise), there is a subset of thepossible modulation combinations that perform optimally, and an evenlarger subset of the possible modulation combinations that performacceptably. Some modulation combinations impose higher demands upon theunderlying hardware than other combinations. For example, modulationcombinations with higher g values typically require power amplifiersthat may slew more rapidly and concomitantly analog to digitalconverters or ADC that may sample the signal more rapidly. Since spiralbased signals are not periodic, the Nyquist sampling theorem does notapply and thus the band-limited received signal must be measured atmultiple points in order to determine its shape. In general, theperformance of spiral based communications may be arbitrarily improvedby increasing the number of samples taken at the receiver. However, asthe sample rate increases, so too do the demands on the ADC andsubsequent digital filters. Thus it is possible to trade offcommunications performance with hardware cost and the amount of powerrequired to run the ADC and subsequent digital filters. This hasenormous implications for certain types of communications applications,as will be described.

It should be apparent that spiral based communications offers tremendousflexibility when compared to traditional forms of communications. Whilethis flexibility may be exploited in the design of any givencommunications channel, it is particularly beneficial when implementedin a software defined radio or SDR. In a SDR, some or all of thefeatures that traditionally were implemented in hardware are insteadimplemented in software such as non-transitory storage media. Typicallythis includes functions such as mixing, demodulation, modulation,filtering, phase locking and so on. Indeed, a state of the art SDRincludes a powerful microprocessor, high speed ADC, high speed DAC, apower amplifier and an antenna. All of the radio functions areimplemented in the microprocessor's non-transitory storage media. Assuch, an SDR is the perfect vehicle for exploiting the flexibility ofspiral based communications.

SUMMARY OF THE INVENTION

Embodiments of the present invention relate to combining the markedlydifferent characteristics of different spiral modulation sets with thedynamic configurability of spiral based communications so as to improvethe performance of various types of communication channels.

In a first exemplary embodiment of the invention, a spiral basedcommunications channel may change its modulation set as channelconditions change so as to maintain channel performance.

In a second exemplary embodiment of the invention, the dynamicconfigurability of spiral based communications may be exploited so as tominimize average power consumption of the transmitter.

In a third exemplary embodiment of the invention, the dynamicconfigurability of spiral based communications may be exploited so as tominimize peak power consumption of the transmitter.

In a fourth exemplary embodiment of the invention, the dynamicconfigurability of spiral based communications may be exploited so as tominimize average power consumption of the receiver.

In a fifth instance of the invention, the dynamic configurability ofspiral based communications may be exploited so as minimize averagepower consumption across the communications network.

BRIEF DESCRIPTION OF THE DRAWINGS

Advantages of embodiments of the present invention will be apparent fromthe following detailed description of the exemplary embodiments thereof,which description should be considered in conjunction with theaccompanying drawings in which like numerals indicate like elements, inwhich:

FIG. 1 is an exemplary diagram showing a block diagram of a QAMmodulator.

FIG. 2 is an exemplary diagram showing a constellation diagram for BPSK.

FIG. 3 is an exemplary diagram showing a constellation diagram for 16QAM.

FIG. 4 is an exemplary diagram showing a constellation diagram for 32QAM.

FIG. 5 is an exemplary diagram showing a constellation diagram for 64QAM.

FIG. 6 is an exemplary diagram showing a graph of a 8-PSK constellationdiagram

FIG. 7 is an exemplary diagram showing a graph of a bit rate curve forBPSK, QPSK, 8-PSK and 16-PSK channels.

FIG. 8 is an exemplary diagram showing a block diagram of a softwaredefined radio.

FIG. 9 is a flowchart showing a method for utilizing a bit stream forspiral based encoding.

DETAILED DESCRIPTION

Aspects of the present invention are disclosed in the followingdescription and related figure directed to specific embodiments of theinvention. Those skilled in the art will recognize that alternateembodiments may be devised without departing from the spirit or thescope of the claims. Additionally, well-known elements of exemplaryembodiments of the invention will not be described in detail or will beomitted so as not to obscure the relevant details of the invention.

As used herein, the word “exemplary” means “serving as an example,instance or illustration.” The embodiments described herein are notlimiting, but rather are exemplary only. It should be understood thatthe described embodiments are not necessarily to be construed aspreferred or advantageous over other embodiments. Moreover, the terms“embodiments of the invention”, “embodiments” or “invention” do notrequire that all embodiments of the invention include the discussedfeature, advantage or mode of operation.

FIG. 1 is an exemplary diagram showing a block diagram 100 of a QAMmodulator. The QAM modulator 100 may produce a QAM signal 105. The QAMmodulator 100 may include a first finite impulse response or first FIRcosine filter 110, a cosine multiplexor 120, a numerically controlledoscillator 130, a second finite impulse response or second FIR cosinefilter 140 and a sine multiplexor 150. The first finite impulse responseor first FIR cosine filter 110 may receive an input signal 112 such asan I-input signal 114 and filter the input signal. The cosinemultiplexor 120 may receive the filtered input signal 112′ and a signalfrom the numerically controlled oscillator 130 and forward the selectedinput into a single signal 122. The numerically controlled oscillator130 may receive a signal from a phase increment source 132 that couldgenerate waves with different frequencies. The second FIR cosine filter140 may receive an input signal 142 such as a Q-input signal 144 andfilter the input signal 142. The sine multiplexor 150 may receive thefiltered input signal 142′ and a signal from the numerically controlledoscillator 130 and forward the selected input into a single signal 152.The sum of 122 and 152 may be the QAM signal 105.

FIG. 2 is an exemplary diagram showing a constellation diagram 200 forbinary phase shift keying or BPSK. The constellation diagram 200 mayinclude an X-axis 210, a Y-axis 220 and a pair of points 230. The X-axis210 may include a first point 232 of a pair of points 230. The X-axis220 may include a second point 234 of a pair of points 230. The pair ofpoints 230 may represent a pair of constellation points 236.

FIG. 3 is an exemplary diagram showing a constellation diagram 300 for16 QAM. The constellation diagram 300 may include an X-axis 310, aY-axis 320 and a plurality of points 330. The X-axis 310 may include aplurality of predetermined Quadrature or Q quantities 312. The Y-axis320 may include a plurality of predetermined In-phase or I quantities322. The pair of points 330 may represent approximately sixteenconstellation points 332.

FIG. 4 is an exemplary diagram showing a constellation diagram 400 for32 QAM. The constellation diagram 400 may include an X-axis 410, aY-axis 420 and a plurality of points 430. The X-axis 410 may include aplurality of predetermined Quadrature or Q quantities 412. The Y-axis420 may include a plurality of predetermined In-phase or I quantities422. The points 430 may represent approximately thirty-two constellationpoints 432.

FIG. 5 is an exemplary diagram showing a constellation diagram 500 for64 QAM. The constellation diagram 500 may include an X-axis 510, aY-axis 520 and a plurality of points 530. The X-axis 510 may include aplurality of predetermined Quadrature or Q quantities 512. The Y-axis520 may include a plurality of predetermined In-phase or I quantities522. The points 530 may represent approximately sixty-four constellationpoints 532.

FIG. 6 is an exemplary diagram showing a graph 600 of a 8-PSKconstellation diagram. The graph may include an X-axis 610, a Y-axis 620and a plurality of points 630. The X-axis 610 may include a plurality ofpredetermined Quadrature or Q quantities 612. The Y-axis 620 may includea plurality of predetermined In-phase or I quantities 622. The points630 may represent approximately eight constellation points 632.

FIG. 7 is an exemplary diagram showing a graph 700 of a plurality ofbit-error rate curves. The graph 700 includes a BPSK bit-error ratecurve 710, a QPSK bit-error rate curve 720, a 8-PSK bit-error rate curve730 and a 16-PSK bit-error rate curve 740. The BPSK bit-error rate curve710 may be for a AWGN channel 705. The QPSK bit-error rate curve 720 maybe for a AWGN channel 705. The 8-PSK bit-error rate curve 730 may be fora AWGN channel 705. The 16-PSK bit-error rate curve 740 may be for aAWGN channel 705.

FIG. 8 is an exemplary diagram showing a block diagram of softwaredefined radio or SDR 800, supporting both transmission and reception.FIG. 8 is a block diagram of a typical SDR 800 having a memory system810, a microprocessor 820, a digital to analog converter 830, a poweramplifier 840, an antenna 850 and an analog to digital converter 860.The memory system 810 may store a plurality of modulation sets 812. Thememory system 810 may permit the modulation sets 812 to beinstantaneously switched. The microprocessor 820 may be in communicationwith the memory system 810 via a bus 815. The microprocessor 820 mayinclude a non-transitory storage media 822 where one or more radiofunctions may be implemented and a transmitter 824 to generate a bitstream. The non-transitory computer storage media 822 may dynamicallyselect one or more spiral modulation sets to accommodate one or morechanging channel conditions and may minimize average power consumptionof the one or more spiral modulation sets so as to minimize averagetransmitted power and minimize power consumption. The one or more spiralmodulation sets for a given channel impairment may be known a priori.Each of the one or more spiral modulation sets systematically may betried to determine the one or more spiral modulation sets that workoptimally. A heuristic algorithm may determine the one or more optimalspiral modulation sets. The one or more spiral modulation sets may befor Additive White Gaussian Noise or AWGN impaired channels to improve areceived signal at one or more frequencies. The average transmittedpower may be minimized and the one or more spiral modulation sets maychange to minimize the average transmitted power. A plurality ofmodulation set data may be computed off line and stored in the memorysystem. The microprocessor 820 may segment the bit stream received fromthe modulation sets 812 residing on the memory system 810 according tomodulation alphabet size. The microprocessor 820 may decide a priori howmany of a plurality of samples will be transmitted per symbol. Forsignal transmission, the digital to analog converter 830 may be incommunication with the microprocessor 820 via the bus 815. The digitalto analog converter 830 may receive a plurality of spiral based symbolwaveforms from the microprocessor 820. The digital to analog converter830 may be driven by a bandwidth limiting filter 832 whose output mayfeed into a radio frequency or RF stage. The power amplifier 840 may bein communication with the digital to analog converter 830 via the bus815. The power amplifier 840 may be driven by the bandwidth limitingfilter 832. The antenna 850 may be in communication with the poweramplifier 840 via the bus 815 . . . . The analog to digital converter860 may provide signal reception, digitize an analog signal from theantenna 850 and feed the digitized analog signal back to themicroprocessor 820.

While it is common for a SDR to perform a multitude of transformationson the data to be transmitted, including encryption, interleaving andforward error correction, these transformations are not germane to thepresent invention. Rather, as such transformations are known to onehaving skill in the art, the descriptions thereof are omitted, and it isassumed that all requisite transformations have been performed resultingin a bit stream that needs to be transmitted. Once this stage has beenreached, an SDR may perform the following steps or method in order totransmit the bit stream utilizing spiral based encoding.

FIG. 9 is an exemplary diagram showing a method 900 for transmitting abit stream utilizing spiral based encoding. The method 900 may includethe steps of transmitting a signal from one or more spiral modulationsets residing on a memory system of the software defined radio, thesignal from one or more spiral modulation sets includes the bit streamsegmented by a microprocessor according to modulation alphabet size 910and receiving the signal from one or more spiral modulation sets,wherein the signal from one or more spiral modulation sets are filteredand then fed to an analog to digital converter, where the signal fromthe one or more spiral modulation sets may be digitized and are fed tothe microprocessor 920. The transmitting step 910 may dynamically selectone or more spiral modulation sets to accommodate one or more changingchannel conditions and may minimize average or peak power consumptionand the one or more spiral modulation sets so as to minimize an averagetransmitted power and minimize power consumption. The one or more spiralmodulation sets for a given channel impairment may be known a priori.Each of the one or more spiral modulation sets systematically may try todetermine the one or more spiral modulation sets that work optimally. Aheuristic algorithm may determine the one or more optimal spiralmodulation sets. The receiving step 920 may utilize one or more spiralmodulation sets that may be for Additive White Gaussian Noise or AWGNimpaired channels to improve recognition of a received signal at one ormore frequencies. The average transmitted power may be minimized and theone or more one or more spiral modulation sets may change to minimizethe average transmitted power. A plurality of modulation set data may becomputed off line and stored in the memory system.

The bit stream may be segmented by the microprocessor according to themodulation alphabet size M. Thus for example, if the alphabet size M isapproximately 64, then the bit stream is segmented into approximately 6bit segments, since 2⁶=64. Based on the desired performance level, powerconsumption, hardware cost etc., the transmitter microprocessor decidesa priori how many samples will be transmitted per symbol. Typical valuesare approximately 16 . . . 256. Based on the channel conditions,available power, regulatory limits, application limits and so on, thetransmitter microprocessor decides upon a modulation set. Although inprinciple the number of modulation sets is unlimited, a typical radiowill have between approximately 1 and 1024 modulation sets. The valueV_(t) to be transmitted at any instant t, for a modulation set M_(i),symbol S_(j) and symbol time T_(k), is determined by performing an indexinto a 3-dimensional array located in memory system, whereV_(t)=Modulation[i]·Symbol[j]·Time[k]. Successive V_(t) are thentypically passed through a bandwidth limiting filter, thecharacteristics of which are not relevant to the present invention. Theoutput of the bandwidth limiting filter is utilized to drive a DAC,whose output in turn may be utilized to drive a power amplifier which inturn may drive an antenna. In some instances the power amplifier willdirect a cable.

A signal transmitted in the described manner may be received by areceiver. The receiver may perform the following steps. The analogwaveform may be received by the antenna, possibly filtered and amplifiedand then fed to an ADC where it may be digitized and the digital samplesfed to a microprocessor. Based on the desired performance level, powerconsumption, hardware costs, etc., the receiver microprocessor decides apriori how many samples will be taken per received symbol. Typicalvalues are approximately 16 . . . 256. Note it is common, but notrequired, that the transmitter and receiver utilize the same number ofsamples. The received samples are usually normalized to a referencepower level. This set of normalized received samples may be consideredthe received vector R. Within the receiver there are symbol templatesincluding a two-dimensional array stored in memory indexed by modulationtype and symbol. The elements of this array are a vector of the expectedset of received samples for the given modulation type and symbol number.Denote the expected vector for modulation i and symbol j to be E_(ij).The receiver then compares the received vector R with each of thepossible expected vectors E_(ij) (j=0 . . . M−1). The comparison betweenthe received symbol and templates may be typically performed bycomputing the vector dot product of R with E_(ij) for all j andselecting the product with the largest value. However, the exact methodis not germane except in the sense that it involves looking up atemplate from memory.

It should be apparent from this description that changing the spiralmodulation set requires merely that an index into a lookup table bechanged for both the transmitter and the receiver. As a result, a systemmay change spiral modulation sets at an arbitrary rate. In practice, onedoes not change the spiral modulation set during a symbol transmission,but rather immediately prior to transmitting a new symbol. The frequencywith which the spiral modulation set is changed may be entirelyapplication dependent. The implications of this will now be described invarious exemplary instances of the invention.

In a first exemplary embodiment of the invention that accommodateschanging channel conditions, the SDR may dynamically select its spiralmodulation set so as to accommodate changing channel conditions. Notethat in general, selection of the optimal spiral modulation set will bedone with a fixed alphabet size M. That is, for a given desiredthroughput, which is a function of M, the objective is to determine theoptimal spiral modulation set. For channels with serious impairment, itmay of course be necessary to reduce the bit rate so as to achieve anacceptable Bit Error Rate or BER. An estimate of the expected BER for agiven alphabet and channel conditions may be obtained by priorsimulation or physical transmission tests.

For AWGN channels, a third approach to determining expected BER is toutilize a variant of a geometric approach. It is known to the art thatband limited non-periodic symbol waveforms may be represented inprinciple by an unlimited sequence of independent points transmitted atthe frequency of the channel's baseband bandwidth B. This contrasts withtraditional periodic symbol waveforms, for which by the Sampling Theoremshows that at most two independent points may be transmitted atfrequency B.

Applying Shannon's geometric approach on a per-symbol, rather thanper-complete-signal basis, each band limited non-periodic symbolwaveform w may be represented by a point in a space of dimension d,where d is the number of independent points in the specification of w.The expected BER for a given level of AWGN is proportional to theprobability that the specified level of noise will displace a symbolmore than half the distance to its nearest neighbor, thereby causing asymbol reception error. This probability may be determined from aGaussian function parameterized by the distance between symbols and thelevel of noise.

Consider by way of example a communications channel between two mobiledevices such as vehicles utilized by the emergency services. For anapplication such as this it is possible to identify a plethora ofdifferent channel conditions. For example, the vehicles are movingrelative to each other at high speed, resulting in a communicationschannel subject to significant fading. The vehicles are stopped in anurban environment resulting in a communications channel that may besubject to significant multi-path interference. The vehicles are in arural setting separated by large distances such that the communicationschannel may be subject to significant AWGN. The vehicles are out in anadverse weather conditions where rain fade and burst noise fromlightning are significantly impacting the communications channel. Inthis example, the radios utilized in this communications channel containa multitude of different spiral modulation sets that may be selected onthe fly.

In a first instance of this example, the optimal spiral modulationset(s) for a given channel impairment are known a priori. In this casethe receiver and transmitter agree on what the impairment is and switchto the agreed upon modulation set for the specific impairment. Thisapproach may be useful when it is possible to easily distinguish betweendifferent impairments.

In a second instance of this example, the receiver and transmittersystematically try each of the different spiral modulation sets in orderto determine those that work optimally. Having agreed upon an optimalmodulation set, the radios may utilize that set indefinitely, utilizethat set until the BER exceeds a certain level, at which point theradios recommence a systematic search of the spiral modulation sets todetermine the new optimal spiral modulation set, periodically perform asystematic search of the spiral modulation sets to determine the newoptimal spiral modulation set, irrespective of the current BER andcontinuously perform a systematic search of the spiral modulation setsto determine the new optimal spiral modulation set. This approach may beuseful when the communications channel is not in continuous use, andthus the channel may be available for experimentation.

In a third instance of this example, the receiver and transmitterutilize a heuristic algorithm to determine the optimal spiral modulationset. By way of example, the heuristic algorithm may determine thecharacteristics of the channel impairment, and utilize this knowledge toperform a systematic search across a limited number of spiralmodulations sets. Having agreed upon an optimal spiral modulation set,the radios may utilize that set indefinitely until the BER exceeds acertain level, at which point the radios recommence a new heuristicsearch of the spiral modulation sets to determine the new optimal spiralmodulation set, periodically perform a heuristic search of the spiralmodulation sets to determine the new optimal spiral modulation set,irrespective of the current BER and continuously perform a heuristicsearch of the spiral modulation sets to determine the new optimal spiralmodulation set. This approach may be useful when the communicationschannel is not in continuous use, and thus the channel may be availablefor experimentation. It should be apparent to one skilled in the artthat any number of algorithms may be utilized to determine the optimalmodulation set for a given set of channel conditions and that the threeexamples given above are merely illustrative of what is possible.

For traditional modulations such as QAM, it is trivial to determine theGray coding. For spiral based modulation, the Gray coding strategy for agiven symbol set is not obvious. Because of the inherent noiseresistance built into spiral based communication, it is not necessary toeven utilize Gray coding. This arises because if the symbol error rateis zero, then the bit error rate is also zero, regardless of whetherGray coding, binary coding, or random coding is utilized.

In a second exemplary embodiment of the invention, the average powerconsumption of the transmitter is minimized and the SDR may change itsmodulation set so as to minimize the average transmitted power and thusminimize the transmitter's power consumption. Consider a communicationschannel in which the receiver is receiving a signal with more thanadequate noise margin, such that the transmitter could safely transmitat reduced power. If the receiver conveys this information to thetransmitter, then in classical transmitter design, the power output ofthe transmitter would be reduced by attenuating the magnitude of thesignal fed into the power amplifier. This approach requires the presenceof programmable gain (e.g., attenuator) stages in the transmit signalpath.

With spiral based modulation, an alternative approach is possible. Thecrest factor C of a signal is defined to be the ratio of the peak to theroot mean square or RMS amplitude. This is sometimes referred to as thepeak-to-average ratio or PAR. The peak to average power ratio or PAPR isthe ratio of the peak amplitude squared (P) to the RMS amplitude squared(A). Thus PAPR=P/A=C² and alternatively A=P/C². For spiral modulation,the crest factor of the signals may be adjusted over a large dynamicrange by adjusting the factor g in Equation 3. Thus for transmitterswith a fixed Peak power P, it is possible to reduce the averagetransmitted power A simply by changing the spiral modulation set suchthat the crest factor C is increased. In a practical system, changingthe spiral modulation set will of course have additional impacts on thecommunications channel performance. However provided these additionalchanges still result in adequate performance, changing the modulationset so as to increase the crest factor is a viable mean of reducingtransmitter power consumption.

In a third exemplary embodiment of the invention, the averagetransmitted power is maximized and the SDR may change its modulation setso as to maximize the average transmitted power. Consider acommunications channel in which the receiver is receiving a signal withinsufficient noise margin, such that the transmitter needs to transmitat an increased power level for reliable communications. If the receiverconveys this requirement to the transmitter, then in classicaltransmitter design, the power output of the transmitter would beincreased by amplifying the magnitude of the signal fed into the poweramplifier. This approach requires the presence of programmable gain(e.g., attenuator) stages in the transmit signal path. However, if theamplifier is already at maximum gain, then the transmitter has no optionother than to reduce its bit rate by, for example switching from QAM64to QPSK modulation.

With spiral modulation, an alternative approach is possible. Asexplained above, P/A=C². For applications where the peak power of thetransmitter is limited (e.g., perhaps by regulatory fiat, or moreprosaically because the transmitter's battery voltage is dropping), thenit is possible to increase the average transmitted power while keepingthe peak power fixed by choosing a spiral modulation set where the CrestFactor is minimized. Note that this may be done without changing the bitrate over a considerable dynamic range. In the limit of course, it isalways necessary to reduce the bit rate.

In a fourth exemplary embodiment of the invention, the receiver powerconsumption may be minimized and the receiver may change its samplingrate and/or the transmitter changes its modulation set so as to minimizethe average power consumption of the receiver. With spiral basedmodulation, for AWGN impaired channels, it is possible to improve theSNR by sampling the received signal at higher frequencies. As thesampling rate increases, the receiver must perform commensurately moreanalog-digital converter readings and run each additional sample throughvarious digital filters. Both of these operations consume considerablepower. Consequently, the power consumption of the receiver is a functionof the sampling rate.

Consider a communications channel in which the receiver is receiving asignal with sufficient noise margin. In order to minimize its powerconsumption the receiver may elect to reduce its sampling rate such thatthe SNR is reduced, but is still acceptable. If the receiver's powerconsumption is still higher than desirable (e.g., possibly because itsbattery is failing), then the receiver could request that thetransmitter change its spiral modulation set, such that the SNR isincreased sufficiently that the receiver could in turn further drop itssampling rate and thus its power consumption.

In a fifth exemplary embodiment of the invention, the network powerconsumption may be minimized and the modulation set and the receiversampling rates may be chosen so as to minimize the total powerconsumption across the communications network. It should be apparentthat the second, third and fourth exemplary embodiments of the inventionare interdependent. So while the previous embodiments have consideredminimizing the power consumption of either the transmitter or thereceiver without regard to the effect on the other party, it should beapparent that there are modulation sets that, while not necessarilyminimizing the power consumption of the transmitter or the receiver, dominimize the power consumption of the communications channel as a whole.This is particularly true for a communications network in which atransmitted signal is received by many receivers (e.g., point tomulti-point).

Determining the optimal modulation set so as to minimize network powerconsumption is a classic linear programming problem in which theparameter to be minimized (e.g., network power) is subject to peak powerof the transmitter, average power of the transmitter, minimum SNR ateach receiver and available power at each receiver. It should beapparent that for many real networks, particularly where the radios arebattery powered, the optimal solution to this problem is dynamic andthus the computation needs to be performed regularly.

The foregoing description and accompanying figures illustrate theprinciples, one or more embodiments and modes of operation of theinvention. However, the invention should not be construed as beinglimited to the particular embodiments discussed above. Additionalvariations of the embodiments discussed above will be appreciated bythose skilled in the art.

Therefore, the above-described embodiments should be regarded asillustrative rather than restrictive. Accordingly, it should beappreciated that variations to those embodiments may be made by thoseskilled in the art without departing from the scope of the invention asdefined by the following claims.

What is claimed is:
 1. A software defined radio designed fornon-periodic signals, comprising: a memory system storing a plurality ofmodulation sets; a microprocessor in communication with the memorysystem via a bus, the microprocessor includes a non-transitory storagemedia where one or more radio functions are implemented and atransmitter to generate a bit stream, the microprocessor segments thebit stream received from the non-periodic modulation sets stored on thememory system according to modulation alphabet size; a digital to analogconverter in communication with the microprocessor via the bus, thedigital to analog converter receives a plurality of spiral basedmodulations from the microprocessor, after a bandwidth limiting filteris applied, and the digital to analog converter feeds into a radiofrequency stage; a power amplifier in communication with the digital toanalog converter via the bus, the power amplifier boosting the radiofrequency stage signal; an antenna receiving the boosted radio frequencystage, the antenna is driven by the boosted radio frequency stage by thebandwidth limiting filter; and an analog to digital converter incommunication with the power amplifier via the bus, the analog todigital converter provides signal reception, digitizes the boosted radiofrequency stage from the antenna and feeds the digitized analog signalback to the microprocessor.
 2. The software defined radio according toclaim 1, wherein the memory system permits the modulation sets to beinstantaneously switched.
 3. The software defined radio according toclaim 1, wherein the microprocessor decides a priori the sequence oftransitions between modulation sets.
 4. The software defined radioaccording to claim 1, wherein the non-transitory storage mediadynamically selects a spiral modulation set to accommodate one or morechanging channel conditions.
 5. The software defined radio according toclaim 4, wherein the one or more spiral modulation sets for a givenchannel impairment are known a priori.
 6. The software defined radioaccording to claim 4, wherein each of the one or more spiral modulationsets are systematically tried to determine the one or more spiralmodulation sets that work optimally.
 7. The software defined radioaccording to claim 6, wherein a heuristic algorithm determines the oneor more optimal spiral modulation sets.
 8. The software defined radioaccording to claim 4, wherein the one or more spiral modulation sets aredesigned for a plurality of Additive White Gaussian Noise impairedchannels to improve a received signal at one or more frequencies.
 9. Thesoftware defined radio according to claim 1, wherein the non-transitorystorage media minimizes an average power consumption and the modulationsets so as to minimize an average transmitted power and minimize powerconsumption.
 10. The software defined radio according to claim 9,wherein the average transmitted power is maximized and the modulationsets are changed to maximize the average transmitted power.
 11. Thesoftware defined radio according to claim 1, wherein a plurality ofmodulation set data is computed off line and stored in the memorysystem.
 12. A method for utilizing a bit stream for spiral basedencoding, comprising: transmitting a signal from one or more spiralmodulation sets residing on a memory system of a software defined radio,the signal from one or more spiral modulation sets includes the bitstream segmented by a microprocessor according to modulation alphabetsize; and receiving the signal from one or more spiral modulation sets,wherein the signal from one or more spiral modulation sets are filteredand then fed to an analog to digital converter, where the signal fromthe one or more spiral modulation sets is digitized and are fed to themicroprocessor.
 13. The method according to claim 12, wherein based onthe desired performance level, power consumption and hardware cost, themicroprocessor decides a priori how many of a plurality of samples willbe transmitted per symbol.
 14. The method according to claim 12, whereinthe signal from the one or more spiral modulation sets is received by anantenna.
 15. The method according to claim 12, wherein thenon-transitory storage media dynamically selects the one or more spiralmodulation sets to accommodate one or more changing channel conditions.16. The method according to claim 15, wherein the one or more spiralmodulation sets for a given channel impairment are known a priori. 17.The method according to claim 16, wherein an attempt is made todetermine the one or more spiral modulation sets that work optimally.18. The method according to claim 17, wherein a heuristic algorithmdetermines the one or more optimal spiral modulation sets.
 19. Themethod according to claim 15, wherein the one or more spiral modulationsets are for a plurality of Additive White Gaussian Noise impairedchannels to improve a received signal at one or more frequencies. 20.The method according to claim 12, wherein the non-transitory storagemedia minimizes an average power consumption and the one or more spiralmodulation sets are selected so as to minimize an average transmittedpower and minimize power consumption.
 21. The method according to claim20, wherein the average transmitted power is maximized and the one ormore spiral modulation sets are changed to maximize the averagetransmitted power.
 22. The method according to claim 12, wherein aplurality of modulation set data is computed off line and stored in thememory system.
 23. A non-transitory computer storage media havinginstructions stored thereon which, when executed, execute a methodcomprising the steps of: transmitting a signal from one or more spiralmodulation sets residing on a memory system of a software defined radio,the signal includes a bit stream segmented by a microprocessor accordingto modulation alphabet size; and receiving the signal from the one ormore spiral modulation sets, wherein the signal from one or more spiralmodulation sets are filtered and then fed to an analog to digitalconverter, where the signal from the one or more spiral modulation setsis digitized and are fed to the microprocessor.
 24. The non-transitorycomputer storage media according to claim 23, wherein based on thedesired performance level, power consumption and hardware cost, themicroprocessor decides a priori how many of a plurality of samples willbe transmitted per symbol.
 25. The non-transitory computer storage mediaaccording to claim 23, wherein the signal from the one or more spiralmodulation sets is received by an antenna.
 26. The non-transitorycomputer storage media according to claim 23, wherein the non-transitorystorage media dynamically selects the one or more spiral modulation setsto accommodate one or more changing channel conditions.
 27. Thenon-transitory computer storage media according to claim 26, wherein theone or more spiral modulation sets for a given channel impairment areknown a priori.
 28. The non-transitory computer storage media accordingto claim 26, wherein an attempt is made to determine the one or morespiral modulation sets that work optimally.
 29. The non-transitorycomputer storage media according to claim 28, wherein a heuristicalgorithm determines the one or more optimal spiral modulation sets. 30.The non-transitory computer storage media according to claim 23, whereinthe one or more spiral modulation sets are for a plurality of AdditiveWhite Gaussian Noise impaired channels to improve a received signal atone or more frequencies.
 31. The non-transitory computer storage mediaaccording to claim 23, wherein the non-transitory storage mediaminimizes an average power consumption and the one or more spiralmodulation sets so as to minimize an average transmitted power andminimize power consumption.
 32. The non-transitory computer storagemedia according to claim 31, wherein the average transmitted power ismaximized and the one or more spiral modulation sets are changed tomaximize the average transmitted power.
 33. The non-transitory computerstorage media according to claim 23, wherein a plurality of modulationset data is computed off line and stored in the memory system.